(quote /,Ring,Ideal)

R/I -- form a quotient ring.

Here I may be: an element of R; a sequence of elements of R; or a submodule of R^1.

The names of the variables are assigned values in the new quotient ring by automatically running use R, unless R has a name, or one of the rings R is a quotient ring of has a name.

Quotient rings are bulky objects, because they contain a Groebner basis for their ideals, so only quotients of ZZ are remembered forever. Typically the ring created by R/I will be a brand new ring, and its elements will be incompatible with the elements of previously created quotient rings for the same ideal.

i1 : ZZ/2 === ZZ/(4,6)



o1 = true

i2 : R = ZZ/101[t]



o2 = R



o2 : PolynomialRing

i3 : R/t === R/t



o3 = false